FRIEND:Flow Regimes from International Experimental and Network Data (Proceedings of the Braunschweig. _ Conference«, October 1993). IAHS Publ. no. 221, 1994. 315 Probable maximum precipitation in the Upper Harz Mountains O. SCHULZE, R. ROTH & O. PIEPER Institut fur Météorologie mid Klimatologie, Universitàt Hannover, Herrenhàuser str. 2, D-30419 Hannover, Germany Abstract An investigation of maximum floods in relation to extreme precipitation was made in the Harz Mountains, as part of a study of the safety aspects of reservoir installations. The estimation of probable maximum precipitation has been completed for the area of Clausthal- Zellerfeld and the Oder River. To estimate probable maximum precipi­ tation water contents were maximized. This involved humidity maximiza­ tion using the physical relationship between water content of the atmos­ phere and the surface dewpoint and estimating the maximum possible dewpoint, for each duration and season of the year with a double exponential function (Gumbel function) from a long climatological time series. Looking at a family of maximized extreme events the probable maximum precipitation is finally calculated from the absolute maximum values. The resulting depth-area-duration curves show a characteristic profile with a rapid increase for short precipitations up to 3 h and an asymptotic increase for long events. INTRODUCTION In the Harz Mountains many water reservoir installations were constructed for the mining industry. Although the reservoir installations have been stable for a very long time an investigation of stability was necessary to fulfil new safety aspects. The fundamentals of the new safety aspects are based on an estimation of maximum floods and the connection with probable maximum precipitation (PMP). The probable maximum precipitation is defined as probable maximum depth of precipitation on different areas for different durations. In comparison with other meteorological para­ meters the precipitation field is not continuous. Therefore both statistical analysis and the measurements of precipitation are difficult. Also the procedures for estimating PMP are admittedly inexact, and the results are approximations (WMO, 1973). Bartels et al. (1990) estimates probable maximum precipitation in Germany by applying precipitation at one point to an area. This method does not work very well in areas with strong orographic structures because the result varies on random selection of measurement points (Roth & Schulze, 1991). Another method is the maximization of territorial precipitation using the physical relationship between the depth of precipitation and water content of the atmosphere (Hauck, 1983; Breuer & Kreuels, 1985; Ruhe et al, 1985; WMO, 1986; Roth & Schulze, 1991). In this report the results of a PMP investigation for the area of Clausthal-Zellerfeld and the Oder river in the Upper Harz Mountains are presented. Distinctions are made between the seasons (summer and winter) in the characteristics of PMP time behaviour. 316 O. Schulze et al. CLUVÎATOLQGICAL SURVEY The Harz Mountains are the northernmost low mountain range in Germany having strong gradients of topography at the northern edge of the mountains and a mean altitude of 700 m a.m.s.l. (summit is the Brocken Mountain, 1142 m a.m.s.L). According to Kôppen's reformed classification of world climates the Harz Mountains belong to the Temperate Oceanic Climate with the exception of the Brocken Mountain which is part of a Temperate Oceanic Mountain Climate. The dominance of general westerly weather situations is shown in the annual and monthly distribution of wind directions having mainly southwesterly winds in autumn and winter, and westerly winds in spring and summer. In the Upper Harz Mountains the annual mean temperature lies between 5° and 6°C with an amplitude of 16 to 17° Kelvin from the coldest to warmest month. The monthly mean temperature is -2°C in January and 14-15°C in July. The mean annual depth of precipitation increases from 700 mm year"1 at the northern edge of the mountains to 1200-1400 mm year"1 in the Upper Harz Mountains. Due to lee effects the annual depth of precipitation is only 600 mm year"1 southeast of the Upper Harz Mountains (this area is called the Lower Harz Mountains). During the summer semi-annual period (April to September) the depth of precipitation lies between 720 mm year"1 and 840 mm year"1 (Upper Harz Mountains) and 300 mm year"1 to 400 mm year"1 in the Lower Harz Mountains. The depth of precipitation in the winter semi-annual period (October to March) is equivalent to the summer (Hoffmeister & Schnelle, 1945; Miiller-Westermeier, 1990). The months with heaviest precipitation are January and July; the mean number of days with precipitation is 230 at the top of Brocken Mountain, 200 in the Upper Harz Mountains and 180 in the foreland of the Harz Mountains. The portion of days with strong convective precipitation is equivalent to the number of days with thunderstorms. On average, thunderstorms occur on 21 days in the Upper Harz Mountains and on 36 days on top of the Brocken Mountain. The number of days with more than 10 mm depth of precipitation in 24 hours during the year is 41 to 44, i.e. monthly between 3 and 5 days. There are between 66 (Clausthal-Zellerfeld) and 106 (on top of the Brocken Mountain) days with snowfall extending over a period from October to May. On average a third of the snow cover lies longer than one week (Reidat, 1963). Comparison between the seasons shows that in winter, half of all precipitation events occur in connection with strong wind velocities independent of wind direction. In other seasons a third of all precipitation events shows the same characteristic. To sum up it can be said that the Upper Harz Mountains are a region with extra­ ordinary heavy precipitation showing the dominant influence of general westerly weather situations through all seasons. MAXIMIZATION OF PRECIPITATION Statistical analysis of heavy precipitation, e.g. KOSTRA (Bartels et al, 1990) allows propositions on return period of precipitation events up to 100 years. Since the extra­ polation over three times shows no threshold, only a physically based maximization Probable maximum precipitation in the Upper Harz Mountains 317 . procedure is useful. For estimating probable maximum precipitation, numerical and empirical procedures exist. Using numerical parameters, a simulation of thermodynamic and convective processes has to be done in detail. The empirical procedure establishes a connection between real precipitation events and an area-depth-duration function. The two aims are that the depth of precipitation is an empirical function of the water content of the atmosphere and that during an extreme event all dynamic parameters should be optimized. In this report the empirical procedures are used. Maximization of water contents was done by humidity maximization using the physical relationship between water content and the surface dewpoint and estimating the maximum possible dewpoint for each duration and season with a double exponential function (Gumbel function) from a long climatological time series. To estimate probable maximum precipitation the following steps are taken: - calculation of territorial precipitation (GBNJ; - calculation of maximum monthly water content (PPWm); - calculation of present water content for each event (PPWJ; - maximization of territorial precipitation (GBNm) as a function of time: GBNm = (PPWm/PPWa) * GBNa (1) - calculation of area-depth-duration function. The two possibilities for determination of territorial precipitation are the arithmetic mean or using the Thiessen polygon method (Thiessen, 1911). The physical connection between water contents of the atmosphere and surface dewpoint is given in equation (2). H Waan = M~* } <l(P,T)dp (2) p with W: water content in mm; pw: density of water; g: gravitational acceleration; q(p,r): mixing ratio (function of pressure and dewpoint). To estimate the return period of extreme dewpoints the approximation to a double exponential distributive function is used. P(X) = exp (-exp(-a (X-jS))) (3) with P(X): probability of event occurrence; a, j3: parameters of distributive function. Using: Y = a(X-J3) (4) then: P(X) = exp(-exp(-F)) [maximum] (5a) and P(X) = 1 -exp(-exp (-Y)) [minimum] (5b) Lowery & Nash (1970) showed that the method of momentum is useful for approxima­ tion of parameters a and j3. After Gumbel (1958) the first momentum for parameter free distribution is the Euler number (p. = 0.5772...) and the second momentum is: a = TCI\J6 (6) 318 O. Schuke et al. It follows for a and /3 in equation (3): a = ir/cryô and 0 = a(x)-K<j6/ir)a(xM (7) Finally the return period Tof event X can be calculated using equation (5a): T(P(x)) = £ +aY Y = -ln(-ln(l-l/7)) (8) (7: return period in years). If the return period is shorter than 1 year, Plate (1982) gives the following solution: T(P(X)) = /3+alnT 0 < T < 1 (9) Using equations (8) and (9) the return period of dewpoints up to 100 years for each month have been calculated from a long climatological time series. It is important to say that the present water content during a precipitation event is evaluated with a maximum persisting 12 h dewpoint (WMO, 1986). RESULTS FOR UPPER HARZ MOUNTAINS A selection of precipitation events which are characterized by releasing a maximum flood in the Harz Mountains or in the forelands were taken for investigation of probable maximum precipitation. Tonn (1982) analysed maximum precipitation in the Harz Mountains for the period 1909 to 1981 distinguishing between summer and winter. The precipitation stations used are Braunlage, Altenau, Bad Grand, Rehberger Graben, Riefensbeek and Dammhaus. All events use a time resolution of 15 minutes for every station. The following extreme precipitation events are used: — maximum flood 13/14 January 1948; — maximum flood 25/26 June 1953; — maximum flood 28 to 30 June 1966; — maximum flood 31 July/ 1 August 1967; — maximum flood 11/12 March 1981; — maximum flood 3/4 June 1981; — heavy precipitation 7 to 9 November 1991.